Algorithm 3 main: GP-Based Hybrid Optimal Feature Decision (HOFD).

01: hybrid = 0; swich(hybrid)    case 0 02:    [score,idx] = RNCA($\mathbf{X}$, $\mathbf{Y}$)    case 1 03:    [score,idx] = F-test($\mathbf{X}$, $\mathbf{Y}$)    case 2 04:    [score,idx] = MRMR($\mathbf{X}$, $\mathbf{Y}$) end Procedure: RNCA($\mathbf{X}$, $\mathbf{Y}$): a training dataset 05: partition training dataset into 5 folds for $i=1,n$ do: where n is the number of the $\lambda$ line space 06:    ${\lambda }_{i,k}$: tuning using 5-fold cross-validation    for $k=1,5$ do: 07:    call NCA($\mathbf{X}$, $\mathbf{Y}$, ${\lambda }_{i,k}$): train NCA for $\lambda$ regularization parameter 08:    compute ${\mathcal{L}}_{i,k}$: record loss values    endfor endfor 09: ${\mathcal{L}}_{\mu }$ = mean(${\mathcal{L}}_{i,k}$): compute average lossvalue 10: ${\lambda }_b=arg{min}_{{\mathcal{L}}_{\mu }}(\mathrm{y}|\mathrm{x},{\lambda }_{i,k},{\mathcal{L}}_{\mu })$: find best ${\lambda }_b$ 11: call NCA($\mathbf{X}$, $\mathbf{Y}$, ${\lambda }_b$, $\zeta$): $\zeta$ = $@({\mathrm{y}}_{\mathrm{i}},{\mathrm{y}}_{\mathrm{j}})1-exp(-|{\mathrm{y}}_{\mathrm{i}}-{\mathrm{y}}_{\mathrm{j}}|)$ 12: return $(\mathrm{w})$ that produces weighted feature vectors 13: [weights, indices] = sort(w, ’decent’): starting from weighted feature set 14: num = 25; where num is number of features 15: rmse = zeros(1, num); 16: $\mathrm{brmse}=\mathrm{zeros}(\mathrm{num},2)$; for $j=1,num-1$ do: 17:    call HOFD( X( :, indices(1:num), y): 18:    return ($\nu$): where $\nu$ is least rmse 19:    $\mathrm{brmse}(\mathrm{j},1)=$ $\nu$; 20:    $\mathrm{brmse}(\mathrm{j},2)=$ num; 21:    num = num − 1; endfor 22: [index] = min($\mathrm{brmse}(:,1)$): 23: num = 25; 24: num = num − index + 1; 25: decision $(\mathrm{indices}(1:\mathrm{num}))$: the best feature subset End procedure